Time-Aware Tensor Decomposition for Missing Entry Prediction

Abstract

Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data. However, existing models for tensor factorization have disregarded the temporal property for tensor factorization while most real-world data are closely related to time. Moreover, they do not address accuracy degradation due to the sparsity of time slices. The essential problems of how to exploit the temporal property for tensor decomposition and consider the sparsity of time slices remain unresolved. In this paper, we propose TATD (Time-Aware Tensor Decomposition), a novel tensor decomposition method for real-world temporal tensors. TATD is designed to exploit temporal dependency and time-varying sparsity of real-world temporal tensors. We propose a new smoothing regularization with Gaussian kernel for modeling time dependency. Moreover, we improve the performance of TATD by considering time-varying sparsity. We design an alternating optimization scheme suitable for temporal tensor factorization with our smoothing regularization. Extensive experiments show that TATD provides the state-of-the-art accuracy for decomposing temporal tensors.